Question: Solve for $x$ and $y$ using elimination. ${6x+2y = 54}$ ${5x-2y = 34}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $2y$ and $-2y$ cancel out. $11x = 88$ $\dfrac{11x}{{11}} = \dfrac{88}{{11}}$ ${x = 8}$ Now that you know ${x = 8}$ , plug it back into $\thinspace {6x+2y = 54}\thinspace$ to find $y$ ${6}{(8)}{ + 2y = 54}$ $48+2y = 54$ $48{-48} + 2y = 54{-48}$ $2y = 6$ $\dfrac{2y}{{2}} = \dfrac{6}{{2}}$ ${y = 3}$ You can also plug ${x = 8}$ into $\thinspace {5x-2y = 34}\thinspace$ and get the same answer for $y$ : ${5}{(8)}{ - 2y = 34}$ ${y = 3}$